A very long bar magnet is placed with its north pole coinciding with the centre of a circular loop carrying an electric current i. The magnetic field due to the magnet at a point on the periphery of the wore is B. The radius of the loop is a. The force on the wire is

Question

A very long bar magnet is placed with its north pole coinciding with the centre of a circular loop carrying an electric current i. The magnetic field due to the magnet at a point on the periphery of the wore is B. The radius of the loop is a. The force on the wire is

Philoid · Accepted Answer

When a bar magnet’s north pole is placed at the centre of a current carrying loop, the magnetic field will get distributed in such a way that the magnetic field will lie in the plane of the loop. So, the magnetic force will be perpendicular to the plane of the loop.

Now, let’s take a current element idl, and the magnetic field associated with it is B. Then the magnetic force on the element is,

On integration throughout the loop of radius a,

Or,

Hence the force acting on the wire is 2πaiB, which is directed in the perpendicular direction of the plane of the loop.